1. Field of the Invention
This invention relates generally to holographic optical elements, and pertains more specifically to a method for realizing an arbitrary wavefront transformation.
2. Description of the Prior Art
In a number of situations, we assume that it is desired to illuminate an object with coherent light such as that from a laser. Since laser beams generally have a rather small cross-sectional diameter, typically on the order of a few millimeters, the beam must be expanded and/or spatially redistributed in order to illuminate most objects.
Where an optical system is only concerned with an expansion of the input light, then a conventional lens can be used. However, where the input wave front should be transformed into an output wave front having arbitrarily specific amplitude and phase so that its energy is redistributed into a more usable form, a conventional lens system is not practical. The problem has been recognized, and optical elements have been fabricated whose end results can only be currently produced by expensive and/or inefficient methods. With the growth in the optics field brought about by the increasingly more common use of lasers, the need for custom wavefront transforming lenses is steadily increasing. Hence, efforts have been made to convert laser beam energy into more appropriately patterned output beams or wave fronts.
One system known to me has involved the conversion of a "donut mode" input laser beam into an output beam with energy at its center. To do this, a pair of optically reflective members were used, one being a cone and the other a "negative cone". However, such a system works well only where a rather simple redistribution of the energy is required. Where a more complicated redistribution is needed, one could not easily grind or otherwise shape the required element which might require locally varying radii of curvature or discontinuous surfaces. The alluded-to prior art system also has the drawback or disadvantage of being quite heavy, as well as being costly and difficult to provide. Where a more complicated redistribution pattern is required, the costs escalate appreciably and sometimes the design proves to be so intricate, such as where abruptly varying curvatures are involved, as to make the needed geometry virtually impossible to realize.
Another system for converting a laser beam involves expanding the beam followed by attenuation at specified spatial locations in order to produce the desired pattern. In this instance, the expanded laser beam is passed through a stencil in order to form an image on the laser beam. While the stencil is quite inexpensive, it has the shortcoming of absorbing very expensive laser light; this necessitates the use of a laser having a far greater power rating than if the absorption were avoided.
Still another method recently made public uses reflecting micro-mirrors to locally alter the direction of propagation of an incident beam, thereby changing the beam intensity at a distance spaced from the optical element. Such a system is being marketed by Spawr Optical Research, Inc., Corona, Calif. 91720. Low-cost optical elements can be produced utilizing the teachings of this system as long as a number are produced from one master. A distinct disadvantage of the marketed system resides in the fact that the object must be located exactly at the target plane since the illumination light will diverge and change its intensity profile at other distances. This system is most useful for delivering laser energy to specific locations. Such a system will not provide suitable illumination for many coherent optical processes, such as interferometry, because of the rapidly varying phase across the incident wave front at the target plane.
Computer-generated holograms are presently being used for various applications, and still another method would be to use a computer-generated hologram to produce the desired wave front. However, as explained in my co-pending application, hereinbefore identified, the efficiency of a computer-generated hologram is quite limited inasmuch as only a few percent of the incident energy goes into the image that is desired. While the efficiency can be improved by using the image as the object for the construction of a second, interferometrically formed hologram, the entire process is still extremely limited in terms of the number of resolution cells in the image. Of course, the costs are compounded because of the need to produce the additional hologram.